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of the monoidal category C {\displaystyle {\mathcal {C}}} . Dually, a comonoid in a monoidal category C {\displaystyle {\mathcal {C}}} is a monoid in...

the triple ( H , Δ , ε ) {\displaystyle (H,\Delta ,\varepsilon )} is a comonoid in the monoidal category ( C , ⊗ , I , α , λ , ρ , γ ) {\displaystyle (C...

and multiplication. This description is useful for understanding how any comonoid object in a monoidal category gives rise to a simplicial object since it...

These maps make any object into a comonoid. In fact, any object in a cartesian monoidal category becomes a comonoid in a unique way. Cartesian monoidal...

are to comonoids. Every set is a comonoid in a unique way, so comonoids are less familiar in abstract algebra than monoids; however, comonoids in the...

corresponds to relational composition of these subspaces. In particular, the Z comonoid (given by the Z spider with one input and two outputs, and the Z spider...

all R, h and A lie in the autonomous monoidal bicategory Comod(V)co of comonoids. Comod(V) = Mod(Vop)coop. Quantum categories were introduced to generalize...

object in C, ( A , δ , ε ) {\displaystyle (A,\delta ,\varepsilon )} is a comonoid object in C, the diagrams and commute (for simplicity the diagrams are...

category of B over an object b. comonad A comonad in a category X is a comonoid in the monoidal category of endofunctors of X. compact Probably synonymous...

coalgebra. Given an object A from a dagger compact category, a basis is a comonoid object ( A , δ , ε ) {\displaystyle (A,\delta ,\varepsilon )} . The two...