homKernel
The hom_kernel tactic is the inverse of kernel_hom: it transforms an
equality written in the monoidal category back to an equivalent equality of
s-finite kernels.
The tactic supports location specifiers like rw or simp:
-
hom_kernel— applies to the goal -
hom_kernel at h— applies to hypothesish -
hom_kernel at h₁ h₂— applies to multiple hypotheses -
hom_kernel at h ⊢— applies to hypothesishand the goal -
hom_kernel at *— applies to all hypotheses and the goal
It is useful to switch back to kernel equations once categorical rewrites are done.
Code
syntax (name := homKernel) "hom_kernel" (ppSpace location)? : tacticActions: Source · Open Issue
New in v4.34.0-rc1-13-gd54da15 (2026-08-21), and its meaning has not changed since.
Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file · open it in the Lean web editor.
Dependency graph
Nothing to draw. Its statement rests on no other declaration in this project, and names nothing from a package left unaudited — so the graph is this declaration alone. That is the answer, not a missing picture.
Audit surface: 0 project declarations, 13 external constants
✓ Proved: no sorry anywhere in its closure
This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.