diff --git a/NEWS.md b/NEWS.md
index 080c415c..cfa91390 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -28,6 +28,7 @@
   - Seurat PCA loadings only contain variable features, not all genes
   - Now properly expands loadings matrix to include all genes with zeros for non-variable features
   - Adds warning when rownames don't match var_names during conversion
+- Improve mapping of dimensionality reduction slots during conversion between AnnData, SingleCellExperiment, and Seurat (PR #333)
 
 # anndataR 0.99.2
 
diff --git a/R/as_Seurat.R b/R/as_Seurat.R
index a23b128a..c48fa538 100644
--- a/R/as_Seurat.R
+++ b/R/as_Seurat.R
@@ -589,23 +589,46 @@ as_Seurat <- function(
 # nolint start: object_name_linter object_length_linter
 .as_Seurat_guess_reductions <- function(adata) {
   # nolint end: object_name_linter object_length_linter
+  # Get mappings keyed by AnnData obsm names from centralized location
+  obsm_mappings <- .get_dimred_mapping(from = "anndata_obsm")
+
   purrr::map(adata$obsm_keys(), function(.obsm) {
     if (!is.numeric(as.matrix(adata$obsm[[.obsm]]))) {
       return(NULL)
     }
 
+    # Determine the Seurat reduction name using common mappings
+    seurat_name <- if (.obsm %in% names(obsm_mappings)) {
+      obsm_mappings[[.obsm]]$seurat
+    } else {
+      .obsm
+    }
+
     mapping <- c(
       # Make sure we have valid keys here to avoid warnings later
-      key = SeuratObject::Key(.obsm, quiet = TRUE),
+      key = SeuratObject::Key(seurat_name, quiet = TRUE),
       embeddings = .obsm
     )
-    if (.obsm == "X_pca" && "PCs" %in% names(adata$varm)) {
-      mapping["loadings"] <- "PCs"
+
+    # Check if this obsm has associated loadings in varm
+    if (.obsm %in% names(obsm_mappings)) {
+      dimred_info <- obsm_mappings[[.obsm]]
+      varm_key <- dimred_info$anndata_varm
+      if (!is.null(varm_key) && varm_key %in% names(adata$varm)) {
+        mapping["loadings"] <- varm_key
+      }
     }
 
     mapping
   }) |>
-    setNames(adata$obsm_keys()) |>
+    setNames(purrr::map_chr(adata$obsm_keys(), function(.obsm) {
+      # Use Seurat naming convention for the reduction names
+      if (.obsm %in% names(obsm_mappings)) {
+        obsm_mappings[[.obsm]]$seurat
+      } else {
+        .obsm
+      }
+    })) |>
     purrr::compact()
 }
 
diff --git a/R/as_SingleCellExperiment.R b/R/as_SingleCellExperiment.R
index a482e318..efe587a0 100644
--- a/R/as_SingleCellExperiment.R
+++ b/R/as_SingleCellExperiment.R
@@ -292,20 +292,46 @@ as_SingleCellExperiment <- function(
 # nolint start: object_length_linter object_name_linter
 .as_SCE_guess_reducedDims <- function(adata) {
   # nolint end: object_length_linter object_name_linter
-  purrr::map(adata$obsm_keys(), function(.obsm) {
+
+  # Get mappings keyed by AnnData obsm names from centralized location
+  obsm_mappings <- .get_dimred_mapping(from = "anndata_obsm")
+
+  # Create mapping and name pairs for each obsm key
+  results <- purrr::map(adata$obsm_keys(), function(.obsm) {
     if (!is.numeric(as.matrix(adata$obsm[[.obsm]]))) {
       return(NULL)
     }
 
     mapping <- c(sampleFactors = .obsm)
-    if (.obsm == "X_pca" && "PCs" %in% names(adata$varm)) {
-      mapping["featureLoadings"] <- "PCs"
+
+    # Check if this is a known dimensionality reduction with loadings
+    if (.obsm %in% names(obsm_mappings)) {
+      dimred_info <- obsm_mappings[[.obsm]]
+      if (
+        !is.null(dimred_info$anndata_varm) &&
+          dimred_info$anndata_varm %in% names(adata$varm)
+      ) {
+        mapping["featureLoadings"] <- dimred_info$anndata_varm
+      }
     }
 
-    mapping
+    # Determine the final name: use Bioconductor convention if available
+    final_name <- if (.obsm %in% names(obsm_mappings)) {
+      obsm_mappings[[.obsm]]$sce
+    } else {
+      .obsm
+    }
+
+    list(mapping = mapping, name = final_name)
   }) |>
-    setNames(adata$obsm_keys()) |>
     purrr::compact()
+
+  # Extract mappings and names, then set names
+  result_names <- purrr::map_chr(results, "name")
+  results <- purrr::map(results, "mapping")
+  names(results) <- result_names
+
+  results
 }
 
 # nolint start: object_length_linter object_name_linter
@@ -382,7 +408,9 @@ as_SingleCellExperiment <- function(
     }
 
     loadings <- adata$varm[[varm_key]]
-    rownames(loadings) <- colnames(embedding)
+    # Add rownames (variable names) and colnames to loadings matrix
+    rownames(loadings) <- adata$var_names
+    colnames(loadings) <- colnames(embedding)
   } else {
     loadings <- matrix(nrow = 0, ncol = ncol(embedding))
   }
diff --git a/R/common_dimred_mappings.R b/R/common_dimred_mappings.R
new file mode 100644
index 00000000..c3907116
--- /dev/null
+++ b/R/common_dimred_mappings.R
@@ -0,0 +1,65 @@
+#' Get dimensionality reduction mappings keyed by a specific framework
+#'
+#' @param from Character string specifying which framework to use as keys.
+#'   One of: "sce", "seurat", "anndata_obsm", "anndata_varm", "anndata_uns"
+#' @return A named list where names are the values from the specified framework
+#'   and values are the complete mapping information for each dimred
+#' @noRd
+.get_dimred_mapping <- function(
+  from = c("sce", "seurat", "anndata_obsm", "anndata_varm", "anndata_uns")
+) {
+  from <- match.arg(from)
+
+  all_mappings <- .get_common_dimred_mappings()
+  result <- list()
+
+  for (mapping in all_mappings) {
+    key <- mapping[[from]]
+    if (!is.null(key)) {
+      result[[key]] <- mapping
+    }
+  }
+
+  result
+}
+
+#' Common dimensionality reduction mappings between AnnData, SingleCellExperiment, and Seurat
+#'
+#' This table defines the standard mappings between scanpy/AnnData naming
+#' conventions, Bioconductor/SingleCellExperiment naming conventions, and
+#' Seurat naming conventions for common dimensionality reduction techniques.
+#'
+#' Based on the conventions documented in dr.md:
+#' - AnnData uses "X_pca", "X_tsne", "X_umap" in obsm and "PCs" in varm
+#' - Seurat uses lowercase "pca", "tsne", "umap"
+#' - SingleCellExperiment uses uppercase "PCA", "TSNE", "UMAP"
+#'
+#' @return A list of dimensionality reduction mappings, where each element contains
+#'   the naming conventions across frameworks and associated metadata
+#' @noRd
+.get_common_dimred_mappings <- function() {
+  list(
+    # Core dimensionality reductions with documented naming conventions
+    list(
+      sce = "PCA",
+      seurat = "pca",
+      anndata_obsm = "X_pca",
+      anndata_varm = "PCs",
+      anndata_uns = NULL
+    ),
+    list(
+      sce = "tSNE",
+      seurat = "tsne",
+      anndata_obsm = "X_tsne",
+      anndata_varm = NULL,
+      anndata_uns = NULL
+    ),
+    list(
+      sce = "UMAP",
+      seurat = "umap",
+      anndata_obsm = "X_umap",
+      anndata_varm = NULL,
+      anndata_uns = NULL
+    )
+  )
+}
diff --git a/R/from_Seurat.R b/R/from_Seurat.R
index bcd8605d..f6dadabb 100644
--- a/R/from_Seurat.R
+++ b/R/from_Seurat.R
@@ -414,6 +414,8 @@ from_Seurat <- function(
 # nolint start: object_name_linter object_length_linter
 .from_Seurat_guess_obsms <- function(seurat_obj, assay_name) {
   # nolint end: object_name_linter object_length_linter
+  # Get reverse mappings from centralized location
+  reverse_seurat_mappings <- .get_dimred_mapping(from = "seurat")
 
   obsm_mapping <- c()
 
@@ -424,7 +426,13 @@ from_Seurat <- function(
       next
     }
 
-    obsm_mapping[reduction_name] <- reduction_name
+    # Create mapping: AnnData obsm name -> Seurat reduction name
+    anndata_name <- if (reduction_name %in% names(reverse_seurat_mappings)) {
+      reverse_seurat_mappings[[reduction_name]]$anndata_obsm
+    } else {
+      reduction_name
+    }
+    obsm_mapping[anndata_name] <- reduction_name
   }
 
   obsm_mapping
@@ -433,6 +441,8 @@ from_Seurat <- function(
 # nolint start: object_name_linter object_length_linter
 .from_Seurat_guess_varms <- function(seurat_obj, assay_name) {
   # nolint end: object_name_linter object_length_linter
+  # Get reverse mappings from centralized location
+  reverse_seurat_varm_mappings <- .get_dimred_mapping(from = "seurat")
 
   varm_mapping <- c()
 
@@ -445,7 +455,17 @@ from_Seurat <- function(
         nrow(loadings) == nrow(seurat_obj) &&
         SeuratObject::DefaultAssay(reduction) == assay_name
     ) {
-      varm_mapping[reduction_name] <- reduction_name
+      # Create mapping: AnnData varm name -> Seurat reduction name
+      anndata_varm_name <- if (
+        reduction_name %in%
+          names(reverse_seurat_varm_mappings) &&
+          !is.null(reverse_seurat_varm_mappings[[reduction_name]]$anndata_varm)
+      ) {
+        reverse_seurat_varm_mappings[[reduction_name]]$anndata_varm
+      } else {
+        reduction_name
+      }
+      varm_mapping[anndata_varm_name] <- reduction_name
     }
   }
 
diff --git a/R/from_SingleCellExperiment.R b/R/from_SingleCellExperiment.R
index ec018a85..067abe21 100644
--- a/R/from_SingleCellExperiment.R
+++ b/R/from_SingleCellExperiment.R
@@ -155,11 +155,24 @@ from_SingleCellExperiment <- function(
 # nolint start: object_length_linter object_name_linter
 .from_SCE_guess_obsm <- function(sce) {
   # nolint end: object_length_linter object_name_linter
-  obsm_mapping <- self_name(SingleCellExperiment::reducedDimNames(sce))
+  # Get reverse mappings from centralized location
+  reverse_dimred_mappings <- .get_dimred_mapping(from = "sce")
 
-  if (rlang::is_empty(obsm_mapping)) {
+  sce_names <- SingleCellExperiment::reducedDimNames(sce)
+
+  if (rlang::is_empty(sce_names)) {
     c()
   } else {
+    # Create mapping: AnnData name -> SCE name
+    obsm_mapping <- c()
+    for (sce_name in sce_names) {
+      anndata_name <- if (sce_name %in% names(reverse_dimred_mappings)) {
+        reverse_dimred_mappings[[sce_name]]$anndata_obsm
+      } else {
+        sce_name
+      }
+      obsm_mapping[anndata_name] <- sce_name
+    }
     obsm_mapping
   }
 }
@@ -167,12 +180,25 @@ from_SingleCellExperiment <- function(
 # nolint start: object_length_linter object_name_linter
 .from_SCE_guess_varm <- function(sce) {
   # nolint end: object_length_linter object_name_linter
+  # Get reverse mappings for varm from centralized location
+  reverse_varm_mappings <- .get_dimred_mapping(from = "sce")
+
   varm_mapping <- c()
 
   for (reduction_name in names(SingleCellExperiment::reducedDims(sce))) {
     reduction <- SingleCellExperiment::reducedDim(sce, reduction_name)
     if (inherits(reduction, "LinearEmbeddingMatrix")) {
-      varm_mapping[reduction_name] <- reduction_name
+      # Create mapping: AnnData varm name -> SCE reduction name
+      anndata_varm_name <- if (
+        reduction_name %in%
+          names(reverse_varm_mappings) &&
+          !is.null(reverse_varm_mappings[[reduction_name]]$anndata_varm)
+      ) {
+        reverse_varm_mappings[[reduction_name]]$anndata_varm
+      } else {
+        reduction_name
+      }
+      varm_mapping[anndata_varm_name] <- reduction_name
     }
   }
 
diff --git a/R/known_issues.R b/R/known_issues.R
index 64441927..7ee3b210 100644
--- a/R/known_issues.R
+++ b/R/known_issues.R
@@ -41,6 +41,11 @@ is_known <- function(backend, slot, dtype, process, known_issues = NULL) {
     known_issues <- read_known_issues()
   }
 
+  # Handle empty known_issues data frame
+  if (nrow(known_issues) == 0) {
+    return(logical(0))
+  }
+
   filt <- rep(TRUE, nrow(known_issues))
 
   if (!is.null(backend)) {
diff --git a/inst/known_issues.yaml b/inst/known_issues.yaml
index 8970b59b..5f6a4283 100644
--- a/inst/known_issues.yaml
+++ b/inst/known_issues.yaml
@@ -1,17 +1 @@
-known_issues:
-  - backend: to_SCE
-    slot:
-      - obsm
-      - varm
-    dtype:
-      - pca
-    process: [convert]
-    error_message:
-      sampleFactors(reducedDims(sce)$pca) (`actual`) not equal to ad$obsm[["X_pca"]] (`expected`).
-
-        `dimnames(actual)` is a list
-        `dimnames(expected)` is absent
-    description: converted sce object has dimnames(), whilst the original anndata does not.
-    proposed_solution: Investigate if this is a problem or not.
-    to_investigate: True
-    to_fix: False
+known_issues: []
diff --git a/tests/testthat/test-as_Seurat.R b/tests/testthat/test-as_Seurat.R
index 56227e3c..5efeeb28 100644
--- a/tests/testthat/test-as_Seurat.R
+++ b/tests/testthat/test-as_Seurat.R
@@ -34,7 +34,7 @@ test_that("as_Seurat retains number of observations and features", {
 for (obs_key in colnames(ad$obs)) {
   test_that(paste0("as_Seurat retains obs key: ", obs_key), {
     msg <- message_if_known(
-      backend = "to_Seurat",
+      backend = "as_seurat",
       slot = c("obs"),
       dtype = obs_key,
       process = "convert",
@@ -56,7 +56,7 @@ for (obs_key in colnames(ad$obs)) {
 for (var_key in colnames(ad$var)) {
   test_that(paste0("as_Seurat retains var key: ", var_key), {
     msg <- message_if_known(
-      backend = "to_Seurat",
+      backend = "as_seurat",
       slot = c("var"),
       dtype = var_key,
       process = "convert",
@@ -75,7 +75,7 @@ for (var_key in colnames(ad$var)) {
 for (layer_key in names(ad$layers)) {
   test_that(paste0("as_Seurat retains layer: ", layer_key), {
     msg <- message_if_known(
-      backend = "to_Seurat",
+      backend = "as_seurat",
       slot = c("layers"),
       dtype = layer_key,
       process = "convert",
@@ -100,7 +100,7 @@ for (layer_key in names(ad$layers)) {
 for (uns_key in names(ad$uns)) {
   test_that(paste0("as_Seurat retains uns key: ", uns_key), {
     msg <- message_if_known(
-      backend = "to_Seurat",
+      backend = "as_seurat",
       slot = c("uns"),
       dtype = uns_key,
       process = "convert",
@@ -115,7 +115,7 @@ for (uns_key in names(ad$uns)) {
 
 test_that("as_Seurat retains pca dimred", {
   msg <- message_if_known(
-    backend = "to_Seurat",
+    backend = "as_seurat",
     slot = c("obsm"),
     dtype = "pca",
     process = "convert",
@@ -125,16 +125,16 @@ test_that("as_Seurat retains pca dimred", {
   skip_if(!is.null(msg), message = msg)
 
   # trackstatus: class=Seurat, feature=test_get_obsm, status=wip
-  expect_true("X_pca" %in% Reductions(seu))
+  expect_true("pca" %in% Reductions(seu))
   expect_equal(
-    Embeddings(seu, reduction = "X_pca"),
+    Embeddings(seu, reduction = "pca"),
     ad$obsm[["X_pca"]],
     ignore_attr = TRUE
   )
 
   # trackstatus: class=Seurat, feature=test_get_varm, status=wip
   expect_equal(
-    Loadings(seu, reduction = "X_pca"),
+    Loadings(seu, reduction = "pca"),
     ad$varm[["PCs"]],
     ignore_attr = TRUE
   )
diff --git a/tests/testthat/test-as_SingleCellExperiment.R b/tests/testthat/test-as_SingleCellExperiment.R
index c1b97257..5f3ddfcc 100644
--- a/tests/testthat/test-as_SingleCellExperiment.R
+++ b/tests/testthat/test-as_SingleCellExperiment.R
@@ -23,7 +23,7 @@ test_that("as_SCE retains nr of observations and features", {
 for (obs_key in colnames(ad$obs)) {
   test_that(paste0("as_SCE retains obs key: ", obs_key), {
     msg <- message_if_known(
-      backend = "to_SCE",
+      backend = "as_SCE",
       slot = c("obs"),
       dtype = obs_key,
       process = "convert",
@@ -44,7 +44,7 @@ for (obs_key in colnames(ad$obs)) {
 for (var_key in colnames(ad$var)) {
   test_that(paste0("as_SCE retains var key: ", var_key), {
     msg <- message_if_known(
-      backend = "to_SCE",
+      backend = "as_SCE",
       slot = c("var"),
       dtype = var_key,
       process = "convert",
@@ -65,7 +65,7 @@ for (var_key in colnames(ad$var)) {
 for (layer_key in names(ad$layers)) {
   test_that(paste0("as_SCE retains layer: ", layer_key), {
     msg <- message_if_known(
-      backend = "to_SCE",
+      backend = "as_SCE",
       slot = c("layers"),
       dtype = layer_key,
       process = "convert",
@@ -124,7 +124,7 @@ test_that("as_SCE works with no x_mapping and no layers_mapping", {
 for (obsp_key in names(ad$obsp)) {
   test_that(paste0("as_SCE retains obsp key: ", obsp_key), {
     msg <- message_if_known(
-      backend = "to_SCE",
+      backend = "as_SCE",
       slot = c("obsp"),
       dtype = obsp_key,
       process = "convert",
@@ -148,7 +148,7 @@ for (obsp_key in names(ad$obsp)) {
 for (varp_key in names(ad$varp)) {
   test_that(paste0("as_SCE retains varp key: ", varp_key), {
     msg <- message_if_known(
-      backend = "to_SCE",
+      backend = "as_SCE",
       slot = c("obsp"),
       dtype = varp_key,
       process = "convert",
@@ -172,7 +172,7 @@ for (varp_key in names(ad$varp)) {
 for (uns_key in names(ad$uns)) {
   test_that(paste0("as_SCE retains uns key: ", uns_key), {
     msg <- message_if_known(
-      backend = "to_SCE",
+      backend = "as_SCE",
       slot = c("uns"),
       dtype = uns_key,
       process = "convert",
@@ -191,7 +191,7 @@ for (uns_key in names(ad$uns)) {
 
 test_that("as_SCE retains pca dimred", {
   msg <- message_if_known(
-    backend = "to_SCE",
+    backend = "as_SCE",
     slot = c("obsm", "varm"),
     dtype = "pca",
     process = "convert",
@@ -199,17 +199,16 @@ test_that("as_SCE retains pca dimred", {
   )
   skip_if(!is.null(msg), message = msg)
 
-  # trackstatus: class=SingleCellExperiment, feature=test_get_obsm, status=wip
-  expect_true("pca" %in% names(reducedDims(sce)))
+  # trackstatus: class=SingleCellExperiment, feature=test_get_obsm, status=done
+  expect_true("PCA" %in% names(reducedDims(sce)))
   expect_equal(
-    sampleFactors(reducedDims(sce)$pca),
-    ad$obsm[["X_pca"]],
-    ignore.attributes = TRUE
+    sampleFactors(reducedDims(sce)$PCA),
+    ad$obsm[["X_pca"]]
   )
 
-  # trackstatus: class=SingleCellExperiment, feature=test_get_varm, status=wip
+  # trackstatus: class=SingleCellExperiment, feature=test_get_varm, status=done
   expect_equal(
-    featureLoadings(reducedDims(sce)$pca),
+    featureLoadings(reducedDims(sce)$PCA),
     ad$varm[["PCs"]]
   )
 })
diff --git a/tests/testthat/test-from_Seurat.R b/tests/testthat/test-from_Seurat.R
index c325f4ea..eb89eadd 100644
--- a/tests/testthat/test-from_Seurat.R
+++ b/tests/testthat/test-from_Seurat.R
@@ -123,13 +123,13 @@ test_that("as_AnnData (Seurat) retains pca", {
 
   # trackstatus: class=Seurat, feature=test_set_obsm, status=wip
   expect_equal(
-    ad$obsm[["pca"]],
+    ad$obsm[["X_pca"]],
     Embeddings(obj, reduction = "pca"),
     ignore_attr = TRUE
   )
 
   # trackstatus: class=Seurat, feature=test_set_varm, status=done
-  expanded_varm_pca <- ad$varm[["pca"]]
+  expanded_varm_pca <- ad$varm[["PCs"]]
   loadings <- Loadings(obj, reduction = "pca")
 
   # check whether rows not in loadings are all zero
@@ -161,7 +161,7 @@ test_that("as_AnnData (Seurat) retains umap", {
   skip_if(!is.null(msg), message = msg)
 
   expect_equal(
-    ad$obsm[["umap"]],
+    ad$obsm[["X_umap"]],
     Embeddings(obj, reduction = "umap"),
     ignore_attr = TRUE
   )
diff --git a/tests/testthat/test-from_SingleCellExperiment.R b/tests/testthat/test-from_SingleCellExperiment.R
index fa3f5c3c..30e6f16f 100644
--- a/tests/testthat/test-from_SingleCellExperiment.R
+++ b/tests/testthat/test-from_SingleCellExperiment.R
@@ -176,16 +176,16 @@ test_that("as_AnnData (SCE) retains pca dimred", {
   # trackstatus: class=SingleCellExperiment, feature=test_set_obsm, status=wip
   expect_true("X_pca" %in% names(ad$obsm))
   expect_equal(
-    sampleFactors(reducedDims(sce)$X_pca),
+    sampleFactors(reducedDims(sce)$PCA),
     ad$obsm[["X_pca"]]
   )
 
   # trackstatus: class=SingleCellExperiment, feature=test_set_varm, status=wip
-  expect_true("X_pca" %in% names(ad$varm))
+  expect_true("PCs" %in% names(ad$varm))
   # AnnData now adds dimnames on-the-fly, but SCE doesn't preserve them
   # So we need to strip dimnames for comparison
-  actual_mat <- ad$varm[["X_pca"]]
-  expected_mat <- featureLoadings(reducedDims(sce)$X_pca)
+  actual_mat <- ad$varm[["PCs"]]
+  expected_mat <- featureLoadings(reducedDims(sce)$PCA)
   dimnames(actual_mat) <- NULL
   dimnames(expected_mat) <- NULL
   expect_equal(
diff --git a/tests/testthat/test-h5ad-read.R b/tests/testthat/test-h5ad-read.R
index 54443378..e3a37a15 100644
--- a/tests/testthat/test-h5ad-read.R
+++ b/tests/testthat/test-h5ad-read.R
@@ -9,7 +9,7 @@ test_that("reading H5AD as SingleCellExperiment works", {
 
 test_that("reading H5AD as Seurat works", {
   skip_if_not_installed("SeuratObject")
-  # TODO: remove this suppression when the to_seurat, from_seurat functions are updated.
+  # TODO: remove this suppression when the as_seurat, from_seurat functions are updated.
   seurat <- suppressWarnings(read_h5ad(file, as = "Seurat"))
   expect_s4_class(seurat, "Seurat")
 })
diff --git a/vignettes/usage_singlecellexperiment.Rmd b/vignettes/usage_singlecellexperiment.Rmd
index ac59ee84..df771ce3 100644
--- a/vignettes/usage_singlecellexperiment.Rmd
+++ b/vignettes/usage_singlecellexperiment.Rmd
@@ -82,8 +82,8 @@ sce_obj <- adata$as_SingleCellExperiment(
   colData_mapping = c("Int", "IntNA"),
   rowData_mapping = c(rowdata1 = "String", rowdata2 = "total_counts"),
   reducedDims_mapping = list(
-    "pca" = c(sampleFactors = "X_pca", featureLoadings = "PCs"),
-    "umap" = c(sampleFactors = "X_umap")
+    "PCA" = c(sampleFactors = "X_pca", featureLoadings = "PCs"),
+    "UMAP" = c(sampleFactors = "X_umap")
   ),
   colPairs_mapping = TRUE,
   rowPairs_mapping = FALSE,
@@ -120,7 +120,7 @@ as_AnnData(
   layers_mapping = c("csc_counts"),
   obs_mapping = c(metadata1 = "Int", metadata2 = "IntNA"),
   var_mapping = FALSE,
-  obsm_mapping = list(X_pca = "X_pca", X_umap = "X_umap"),
+  obsm_mapping = list(X_pca = "PCA", X_umap = "UMAP"),
   obsp_mapping = TRUE,
   uns_mapping = c("Bool", "IntScalar")
 )